Bulk and shear viscosities of a polydisperse hard-sphere fluid

The bulk and shear viscosity expressions for a multicomponent hard-sphere mixture in the Enskog transport theory are generalized to the polydisperse limit. The effect of polydispersity is expressed in terms of correction factors to the monodisperse fluid results. These correction factors have been evaluated for both a log-normal size distribution with the mass-size relation of a power-law form and a log-normal mass distribution with fixed particle size, which is the continuous limit of isotopes.     

A convergent nonequilibrium statistical mechanical theory for dense gases. II. Transport coefficients to first order in the density

Using the two-body distribution function found earlier by the authors with the aid of new boundary conditions, the kinetic equation and the transport coefficients are obtained to zeroth and first order in the density. To zeroth order we recover the Boltzmann kinetic equation. To first order the resulting expressions differ from the ones obtained by Choh and Uhlenbeck, due to effects of the medium.3 Reference 2 will be referred to as I. Here we use the same notation as in I.     

Recent developments in the theory of ionic melts

Summary A brief review is given of the present state of the art in the theory and numerical simulation of ionic melts, and in particular of molten alkali halides. Some recent developments concerning the theoretical evaluation of the static pair structure, the phase diagram and the microscopic dynamics in these melts are discussed. The importance of ionic polarizabilities is stressed. Some perspectives for future work are pointed out in the conclusion. Unité de Recherche Associée 1325 du CNRS.     

Nonlinear hyperbolicity in kinetic theory of a gas mixture

Summary A system of nonlinear hyperbolic conservation equations, arising in the study of an evolution problem of a mixture of gases of interacting particles in the presence of only removal effects, is illustrated. Explicit analytical solutions to such system are obtained and commented on both mathematical and physical grounds.

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Riassunto Nel presente lavoro si illustra un sistema di equazioni iperboliche non lineari di conservazione, che si incontra nello studio di un problema di evoluzione per una miscela di gas di particelle interagenti in presenza di soli effetti di rimozione. Soluzioni analitiche esplicite di tale sistema sono costruite e commentate su base sia matematica che fisica.

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Резюме Рассматривается система нелинейных гиперболических уравнений сошранения, возникающих при исследовании проблемы эволюции смеси газов взаимодействующих частиц в присутствии зффектов удаления. Получаются точные аналитические решения для такой системы. Проводится обсуждение полученных результатов с математической и физической точек зрения

     

An analytical study of space-dependent evolution problems in particle transport theory

Summary Space-dependent evolution problems arising in particle transport theory are analytically studied via a systematic application of the Boltzmann equation. Some explicit solutions, that can improve our knowledge of the spatial effects in such a class of problems, are constructed and briefly commented on a physical ground.

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Riassunto Problemi spaziali di evoluzione che si incontrano nella teoria del trasporto di particelle sono studiati analiticamente per mezzo di una sistematica applicazione dell'equazione di Boltzmann. Alcune soluzioni esplicite, che possono migliorare la nostra conoscenza degli effetti spaziali in tale classe di problemi, sono costruite e commentate brevemente su base fisica.

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Резюме Аналитически, используя уравнение Больцмана, исследуются проблемы пространственной эволюции, зозниакющие в теории переноса частиц. Конструируются некоторые точные решения, которые могут уточнить наше понимание пространственных эффектов в таком классе проблем. Проводится обсуждение этих решений.

     

Mode-coupling effects in the density dependence of the shear viscosities of dense argon and methane

We argue that the density dependence of the shear viscosities of dense argon at 174, 223, and 301 K and of dense methane at 298 K can be understood on the basis of the mode coupling theory for hard spheres, in particular near the fluid-solid phase transition.     

Estimation of transport coefficients of dense hadronic and quark matter

In this study, we calculated transport coefficients including the shear viscosity and electrical conductivity relative to the density of dense hadronic and quark matter. By considering the simple massless limit for the quark matter and two different effective models for the hadronic matter, we estimated the transport coefficients of the two phases separately. Accordingly, density profiles of the transport coefficients were depicted in two parts: the phase-space part and the relaxation time part. From calculating the shear viscosity to density ratio, we also explored the nearly perfect fluid domain of the quark and hadronic matter.     

Longitudinal and bulk viscosities of binary fluid mixtures

Expressions for zeroth, second and fourth sum rules of longitudinal and bulk stress auto correlation functions have been derived for binary fluid mixtures. Longitudinal and bulk viscosities of an Ar–Kr mixture have been calculated using Mori's memory function formalism coupled with the sum rules of longitudinal and bulk stress auto correlation functions. The results obtained are compared with the molecular dynamics simulation. Mass dependence of the longitudinal and bulk viscosities has been studied for different compositions of an isotopic mixture at different densities and temperatures. For very large mass ratio, the longitudinal and bulk viscosities of the isotopic mixture are more dependent on mole fraction than on mass.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

Kinetic theory of nonlinear viscous flow in two and three dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦^3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t^–d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.Supported by National Science Foundation grant No. CHE-73-08856 (to HvB, JRD, and JS) and the Center for Theoretical Physics of the Univ. of Md. (to HvB).On leave from Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

Inflation driven by energy and curvature dependent bulk viscosity

We study the relative rates of expansion in cosmologies admitting curvature dependent and energy dependent bulk viscosity. It is conjectured that curvature dependant bulk viscosity may be a phenomenological way of representing gravitational vacuum polarization around the time of the Planck era.     

Some exact results in kinetic theory

It is shown that for fluids composed of particles interacting with pairwise-additive, spherically symmetric forces, the exact linearized transport equation admits mass, momentum, and kinetic energy as homogeneous solutions and that the kinetic part of the bulk viscosity is identically zero.     

大块金属玻璃Zr41Ti14Cu12.5Ni10Be22.5的流变行为研究

采用静态拉伸方法在连续升温条件下动态地测量了大块金属玻璃Zr41Ti14Cu12.5Ni10Be22.5（Vit1）的黏度随温度的变化关系.在应变速率与温度的关系曲线中，观测到了与玻璃转变和晶化过程相联系的多个应变速率峰.在玻璃转变温度Tg以上，大块金属玻璃Zr41Ti14Cu12.5Ni10Be22.5的过冷液体呈现Newton流体特征，其黏度与温度的关系符合Vogel Fulcher-Tammann (VFT)关系式，拟合得到脆度D*＝36，VFT温度T0＝319K，脆度参数m＝30，这说明Zr41T 关键词： 大块金属玻璃 应变速率 剪切黏度 自由体积     

Melting properties of group-V elements and InSb

Summary In this paper, we study the structural properties of liquid group-V elements (and a compound InSb) and we analyse the differences with their room temperature crystalline phases. Neutron diffraction experiments are performed using short-wavelength neutrons (0.7 ?). We show different melting behaviours of a light element (As) and a heavy element (Sb) under study. Whereas As keeps its coordination three upon melting, Sb is six-coordinated in the melt. Similarly, InSb has a coordination number increasing from 4 to about 6 upon melting. Large entropies of melting are related to important structural variations. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Space distribution and energy straggling of charged particles via Fokker-Planck equation

Summary The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-known Bohr or Bethe formula is found as a first-order approximation of the Fokker-Planck equation. The authors of this paper have agreed to not receive the proofs for correction.     

Electronic fluctuation,the nature of interactions and the structure of liquid metals

Summary Interactions controlling ionic motion and structure in liquid metals can be systematically developed beginning with the ultimate view of such systems as neutral assemblies of nuclei and electrons, and proceeding to standard reduced Hamiltonians reflecting assemblies ofions and electrons. The assumption of electronically rigid ion leads via response methods and pseudopotentials to statically screened ion-ion potentials and beyond. Fluctuations are introduced into this otherwise common viewpoint by relaxing the assumption of electronically rigid ion cores and also by treating electronic response beyond linear order. It is argued that both effects can lead to more attractive pair interactions and possibly to effects much larger than, for example, Friedel oscillations. These contributions are state (i.e. density) dependent and their presence might be expected on the basis of clustering behavior seen for some systems in theirvapour phases. This leads to two limiting viewpoints on the liquid-state structure of such systems, the first as an entirely monoatomic phase but with a pair interaction that is unusual, the second as a system supporting transient clusters whose presence reflects the complexities argued on the basis of a more extended treatment of the electron problem. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1– May, 1989.     

Microscopic approach to shear viscosities of unitary Fermi gases above and below the superfluid transition

Recent experiments on the shear viscosity η in a unitary Fermi gas fail to see the theoretically predicted upturn in η at the lower T. In this Letter, we compute η in a fashion which is demonstrably consistent with conservation laws and, in the process, provide an understanding of recent experiments. We show that this disagreement with prior theories cannot be readily attributed to the trap, since (via edge effects) trap-averaged viscosities will be larger than their homogeneous counterparts. The small values of η we find can be simply understood; they reflect the fact that the Goldstone bosons (phonons) do not couple to transverse probes such as η, and fermionic excitations, which determine the viscosity, are necessarily absent in the ground state.     

Quantum theory of irreversibility

A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N$N$-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix.